MRI is done using two processes. First step, phase and frequency information are measured in K-Space, secondly mathematical computations are carried on the k-space data to reconstruct MRI image. The conventional methods with full k-space are time consuming. The mathematical theory, Compressed Sensing has been used vastly in Magnetic Resonance Imaging for acceleration of imaging process. As it highly exploits data redundancy, i.e. with significant fewer measurements, it produces accurate reconstruction in very short time. In implementation of CS, various algorithms are developed to solve nonlinear system of equations for having better quality of images and speed of reconstruction. For selection of an optimal CS algorithm, a systematic and comparative analysis of these algorithms is necessary. Four algorithms are given in our thesis Conjugate Gradient, RecPF, FCSM and WaTM, which are studied and analyzed on different part of body. Results show that FCSM has less computation time and WaTM has high SNR ratio.